diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -744,7 +744,8 @@ brief overview of basic concepts of the representation theory of Lie algebras.
We should stress, however, that the representation theory of Lie algebras is
only a small fragment of what is today known as representation theory, which is
in general concerned with a diverse spectrum of algebraic and combinatorial
-structures -- such as groups, quivers and associative algebras.
+structures -- such as groups, quivers and associative algebras. An introductory
+exploration of some of this structures can be found in \cite{etingof}.
We begin by noting that any \(\mathcal{U}(\mathfrak{g})\)-module \(V\) may be
regarded as a \(K\)-vector space endowed with a ``linear action'' of
@@ -785,9 +786,10 @@ following definition.
representation of \(\mathfrak{g}\)}.
\end{example}
-It is usual practice to write simply \(X \cdot v\) or \(X v\) for \(\rho(X)
-v\) when the map \(\rho\) is clear from the context. For instance, one might
-say\dots
+Hence there is a one-to-one correspondance between representations of
+\(\mathfrak{g}\) and \(\mathcal{U}(\mathfrak{g})\)-modules. It is usual
+practice to write simply \(X \cdot v\) or \(X v\) for \(\rho(X) v\) when the
+map \(\rho\) is clear from the context. For instance, one might say\dots
\begin{example}\label{ex:sl2-polynomial-rep}
The space \(K[x, y]\) is a representation of \(\mathfrak{sl}_2(K)\) with